Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

22. Dark matter 219
produced non-thermally. At temperatures well above the QCD phase
transition, the axion is massless, and the axion field can take any value,
parameterized by the “misalignment angle” θi. At T < ∼ 1GeV,theaxion
develops a mass ma due to instanton effects. Unless the axion field
happens to find itself at the minimum of its potential (θi = 0), it will begin
to oscillate once ma becomes comparable to the Hubble parameter H.
These coherent oscillations transform the energy originally stored in the
axion field into physical axion quanta. The contribution of this mechanism
to the present axion relic density is [9]
Ωah 2 �
= κa fa/10 12 �1.175 GeV θ 2 i , (22.5)
where the numerical factor κa lies roughly between 0.5 and a few.
If θi ∼O(1), Eq. (22.5) will saturate Eq. (22.1) for fa ∼ 1011 GeV,
comfortably above laboratory and astrophysical constraints [9]; this
would correspond to an axion mass around 0.1 meV. However, if the postinflationary
reheat temperature TR >fa, cosmic strings will form during
the PQ phase transition at T � fa. Their decay will give an additional
contribution to Ωa, which is often bigger than that in Eq. (22.5) [10],
leading to a smaller preferred value of fa, i.e., larger ma. On the other
hand, values of fa near the Planck scale become possible if θi is for some
reason very small.
Weakly interacting massive particles (WIMPs) χ are particles with
mass roughly between 10 GeV and a few TeV, and with cross sections of
approximately weak strength. Their present relic density can be calculated
reliably if the WIMPs were in thermal and chemical equilibrium with
the hot “soup” of Standard Model (SM) particles after inflation. Their
present relic density is then approximately given by (ignoring logarithmic
corrections) [11]
Ωχh 2 � const. ·
T 3 0
M 3 Pl 〈σ 0.1 pb· c
� . (22.6)
Av〉 〈σAv〉 Here T0 is the current CMB temperature, M Pl is the Planck mass, c is
the speed of light, σ A is the total annihilation cross section of a pair
of WIMPs into SM particles, v is the relative velocity between the two
WIMPsintheircmssystem,and〈...〉 denotes thermal averaging. Freeze
out happens at temperature T F � mχ/20 almost independently of the
properties of the WIMP. Notice that the 0.1 pb in Eq. (22.6) contains
factors of T0 and M Pl; it is, therefore, quite intriguing that it “happens”
to come out near the typical size of weak interaction cross sections.
The currently best motivated WIMP candidate is, therefore, the lightest
superparticle (LSP) in supersymmetric models [12] with exact R-parity
(which guarantees the stability of the LSP). Detailed calculations [15]
show that the lightest neutralino will have the desired thermal relic density
Eq. (22.1) in at least four distinct regions of parameter space. χ could be
(mostly) a bino or photino (the superpartner of the U(1) Y gauge boson
and photon, respectively), if both χ and some sleptons have mass below
∼ 150 GeV, or if mχ is close to the mass of some sfermion (so that its relic
density is reduced through co-annihilation with this sfermion), or if 2mχ
is close to the mass of the CP-odd Higgs boson present in supersymmetric
models. Finally, Eq. (22.1) can also be satisfied if χ has a large higgsino
or wino component.